The present invention relates to a method and apparatus for determining the average density or volume percentage of a multicomponent mixture by means of gamma transmission analysis.
Flow engineered transport through pipelines is a very advantageous conveying method, not only for gases or liquids, but also for solids. Because of many advantages, such as simplicity, environmental safety, independence of weather, ease of maintenance and the like, the hydraulic transport of solids has become very widespread in the past decades and is gaining in significance today. Most important is the hydraulic transport of raw materials over long distances, as, for example, the transport of ores and coal over long overland routes or, in the future, the transport of marine raw material deposits (manganese modules, ore slurries and the like) mined in the deep sea.
Compared to all competing conveying systems, hydraulic transportation of solids has interesting economic prospects for large conveying quantities and distances with respect to the specific transportation costs. Prerequisite for reliability and economy of such conveying systems is the control and optimization of the transport parameters.
German Auslegeschrift [Published Patent Application] No. 2,622,175 discloses a method which permits, without contacting the material being transported, determination of the most important conveying stream parameters such as, for example, parts by volume of individual components or average density.
This method is based essentially on the fact that for two substances, p and q, having a sufficiently different atomic number z, the ratio of their gamma absorption coefficients, i.e. .mu..sub.p /.mu..sub.q, in the region of low gamma energies up to about 1.5 MeV exhibits a distinct energy dependence.
In this way it is possible to unequivocally determine the two unknown component shares or volume percentages v.sub.p and v.sub.q of these components by way of a measurement of the transmitted intensities J with and without absorbing body at two different gamma energies, E.sub.1 and E.sub.2, produced by gamma sources, represented in two equations. The "volume percentage" is the percentage, by volume, of the corresponding component in the total mixture.
Since generally the measuring geometry is fixed and thus the length L of the transmission path in the irradiated medium is constant, the third component results as an ancillary product from the marginal condition that the sum of the three volume percentages must be 100%. When this method is used in the hydraulic conveying art, the third component is water (w) or another liquid which generally takes up the space in the conveying pipe left by the solid components p and q. In this case it is advisable not to select, as the reference parameter, the absorber free, or vacuum, intensity but the intensity J.sub.w of the gamma radiation for water, or some other conveying medium, without solids. The two transmission equations for energies E.sub.1 and E.sub.2 are then as follows:
For energy E.sub.1 : ##EQU1## For energy E.sub.2 : ##EQU2## where EQU v.sub.p +v.sub.q +v.sub.w =1. (3) PA0 and, EQU v.sub.q =(LN).sup.-1 [1nt.sub.1 (.mu..sub.p.spsb.2)-1nt.sub.2 (.mu..sub.p.spsb.1 -.mu..sub.w.spsb.1)] (5) PA0 where EQU N=(.mu..sub.p.spsb.1 -.mu..sub.w.spsb.1)(.mu..sub.q.spsb.2 -.mu..sub.w.spsb.2)-(.mu..sub.p.spsb.2 -.mu..sub.w.spsb.2)(.mu..sub.q.spsb.1 -.mu..sub.w.spsb.1).multidot.(6)
and .mu. are the corresponding gamma absorption coefficients.
Solving these equations for v.sub.p and v.sub.q results in EQU v.sub.p =(LN).sup.-1 [-1nt.sub.1 (.mu..sub.q.spsb.2 -.mu..sub.w.spsb.2)+1nt.sub.2 (.mu..sub.q.spsb.1 -.mu..sub.w.spsb.1)](4)
The gamma radiation at two energies can here pass in an advantageous manner through the measuring volume on a common beam axis and thus cover exactly the same volume portions. Different physical structures, which would lead to inhomogeneity errors in transmission of the two energies at different locations, thus produce no effect.
Of course this method can also be used for more than three components. An additional gamma energy is then required for each additional component. One further transmission equation then results in the calculation for each additional component.
Other, less precise, methods of gamma absorptiometry employ only one gamma energy to monitor the conveying stream, preferably with the use of the simple Lambert-Beer theorem, or they do not irradiate the measuring volume on a common beam axis but on separate beam axes, as described by J. S. Watt and W. J. Howarth, in IAEA Report Helsinki, 1972, IAEA/SM-159/1.
All known methods have in common that homogeneity of the multicomponent mixture within the measuring volume is implicitly assumed to exist, i.e. the influence of the particle sizes is assumed to be negligible. However in those cases where the particle sizes are finite, e.g. raw coal, gravel or manganese modules, the analysis may furnish results that differ from reality since, due to the nonlinearity of the law of the attenuation of gamma radiation, the data determined from the transmission equations are systematically falsified.
The nature of this particle size problem will be clarified with the aid of FIGS. 1a and 1b. For the sake of simplicity, there is assumed to be a two-component mixture consisting of the substances, or components, A and B. Component A completely absorbs the gamma radiation and component B is completely transmissive thereof. In the case of essentially homogeneous mixture depicted on the left side of FIG. 1a, complete absorption occurs because no gamma quanta are passed through component A, which is illustrated correctly by the so-called "sandwich model" at the right side of FIG. 1a. In contradistinction thereto, in the case of an inhomogeneous mixture, as depicted on the left side of FIG. 1b, there always exists a finite probability that only part of the gamma radiation is absorbed, in contrast to the complete absorption in the first case. The illustration in the form of the sandwich model then furnishes the wrong image.
From this conceptual model it can be seen that in spite of the same volume concentrations in both mixtures, different residual intensities are measured in the cases of the homogeneous mixture and the inhomogeneous mixture. The inhomogeneity therefore furnishes--seen locally--greatly differing absorption for the gamma rays, depending on the presence and spatial distribution as well as size of the coarse grained particles. Therefore the sandwich model which applies only for homogeneous mixtures cannot always be used.